#include #include #include #include namespace nachia{ namespace prime_sieve_explicit_internal{ std::vector isprime = { false }; // a[x] := isprime(2x+1) void CalcIsPrime(int z){ if((int)isprime.size() *2+1 < z+1){ int new_z = isprime.size(); while(new_z*2+1 < z+1) new_z *= 2; z = new_z-1; isprime.resize(z+1, true); for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){ for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false; } } } std::vector prime_list = {2}; int prime_list_max = 0; void CalcPrimeList(int z){ while((int)prime_list.size() < z){ if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max + 1); for(int p=prime_list_max+1; p<(int)isprime.size(); p++){ if(isprime[p]) prime_list.push_back(p*2+1); } prime_list_max = isprime.size() - 1; } } void CalcPrimeListUntil(int z){ if(prime_list_max < z){ CalcIsPrime(z); for(int p=prime_list_max+1; p<(int)isprime.size(); p++){ if(isprime[p]) prime_list.push_back(p*2+1); } prime_list_max = isprime.size() - 1; } } } bool IsprimeExplicit(int n){ using namespace prime_sieve_explicit_internal; if(n == 2) return true; if(n % 2 == 0) return false; CalcIsPrime(n); return isprime[(n-1)/2]; } int NthPrimeExplicit(int n){ using namespace prime_sieve_explicit_internal; CalcPrimeList(n); return prime_list[n]; } int PrimeCountingExplicit(int n){ using namespace prime_sieve_explicit_internal; if(n < 2) return 0; CalcPrimeListUntil(n); auto res = ::std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin(); return (int)res; } // [l, r) ::std::vector SegmentedSieveExplicit(long long l, long long r){ assert(0 <= l); assert(l <= r); long long d = r - l; if(d == 0) return {}; ::std::vector res(d, true); for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){ long long il = (l+p-1)/p, ir = (r+p-1)/p; if(il <= p) il = p; for(long long i=il; i void DivisorZeta(std::vector& a){ using namespace prime_sieve_explicit_internal; int n = a.size() - 1; for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i*d] += a[i]; } template void DivisorInvZeta(std::vector& a){ using namespace prime_sieve_explicit_internal; int n = a.size() - 1; for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i] += a[i*d]; } template void DivisorMobius(std::vector& a){ using namespace prime_sieve_explicit_internal; int n = a.size() - 1; for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i*d] -= a[i]; } template void DivisorInvMobius(std::vector& a){ using namespace prime_sieve_explicit_internal; int n = a.size() - 1; for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i] -= a[i*d]; } template std::vector GcdConvolution(std::vector a, std::vector b){ assert(a.size() == b.size()); assert(1 <= a.size()); DivisorInvZeta(a); DivisorInvZeta(b); for(int i=1; i<(int)a.size(); i++) a[i] *= b[i]; DivisorInvMobius(a); return a; } template std::vector LcmConvolution(std::vector a, std::vector b){ assert(a.size() == b.size()); assert(1 <= a.size()); DivisorZeta(a); DivisorZeta(b); for(int i=1; i<(int)a.size(); i++) a[i] *= b[i]; DivisorMobius(a); return a; } } #include #include #include using namespace std; using i32 = int32_t; using u32 = uint32_t; using i64 = int64_t; using u64 = uint64_t; #define rep(i,n) for(int i=0; i<(int)(n); i++) const i64 INF = 1001001001001001001; using modint = atcoder::static_modint<998244353>; int main(){ int N,M; cin >> N >> M; vector A(N+1); rep(i,M){ int a; cin >> a; A[a] = 1; } nachia::DivisorInvZeta(A); int ans = 0; rep(i,N+1) if(A[i] % 2 != 0) ans++; cout << ans << endl; return 0; } struct ios_do_not_sync{ ios_do_not_sync(){ std::ios::sync_with_stdio(false); std::cin.tie(nullptr); } } ios_do_not_sync_instance;